Car sometimes does not start

My brother owns a 1991 Buick Park AVenue that sometimes does not start. When you turn the key, it does not tunr over. it does not make any noise's, it jsut doesn't do anything. He recently ahd a new fuel pump sensor put in and had the spark plugs changed, but I don't think this problem is related to any work that has been done. The problem has occured prior to the work being done, and has also occured after the work was performed. it seems to be very intermittant--he can try to start it in the afternoon and ahve nothing, and when I come home from work, it will turn over and start right up.
Is there soemthing going on with the ignition switch, or the sensors in the keys? or is this something else entirely?

clean battery terminals, clean terminal on starter, try different key, check fuses under dash on passegers side.there are 5 fuses on a fuse holder for the computer, and vatts security sys.

Hook voltmeter/indicator between small solenoid S terminal (+) and neg. terminal of battery (-) with long leads so meter can stay on dash. If 12V shows & no sound/start, solenoid is likely bad. If 12V doesn't show up at start, then problem is either ignition switch, neutral start switch, or any wires/connections between them. Happy hunting.

sometimes the neutral saftey switch isnt aligned correctly and it prevents starting. Trying turning the key to start while shifting slowly from park to drive (foot on brake). if the switch is misaligned, you'll likely hit the sweet spot while shifting from park to drive.

I had bought my 91 last fall and over the winter the starter seemed slow and the battery was old so I replaced it. After replacing the battery it still did not seem like it was turning over as fast as other cars that I had owned and then it simply would not turn over at all. I ended up doing a simple replacement of the starter with a rebuilt which was surprisingly easy. After talking to a few other people they had told me that it is not an unusual problem and that the starter will hang up on a bad area and then work later.